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Abstract and Applied Analysis
Volume 1, Issue 2, Pages 203-217
http://dx.doi.org/10.1155/S1085337596000103

The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics

Institute for Mathematics and its Applications, University of Minnesota, Minneapolis 55455–0436, MN, USA

Received 6 April 1996

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We show here the uniform stabilization of a coupled system of hyperbolic and parabolic PDE's which describes a particular fluid/structure interaction system. This system has the wave equation, which is satisfied on the interior of a bounded domain Ω, coupled to a “parabolic–like” beam equation holding on Ω, and wherein the coupling is accomplished through velocity terms on the boundary. Our result is an analog of a recent result by Lasiecka and Triggiani which shows the exponential stability of the wave equation via Neumann feedback control, and like that work, depends upon a trace regularity estimate for solutions of hyperbolic equations.